Question

How do I prove that `(-3, 0), (0,4), (3,0)` are the vertices of an isosceles triangle?

Answer 1

The sides `P1P2=P2P3=5` but `P3P1=3` => `triangle_(P1P2P3)` is isosceles

Explanation:

Find the size of the sides of the triangle and show that two sides are equal but the third one is different than the others.

`P1P2=sqrt((0+3)^2+(4-0)^2)=sqrt(9+16)=sqrt(25)=5`
`P2P3=sqrt((3-0)^2+(0-4)^2)=sqrt(9+16)=sqrt(25)=5`
`P3P1=sqrt((-3-3)^2+(0-0)^2)-=sqrt(9+0)=sqrt(9)=3`

The sides `P1P2=P2P3=5` but `P3P1=3` => `triangle_(P1P2P3)` is isosceles